Google Nexus 7 (2013) — Lost my N7-13 and need to know...

Considering in buying a refurbished one on ebay. It comes with os 4.3 ...would i be able to upgrade to Lollipop 6.01? Also, whenever there was such an upgrade, it came on my 'lost' tablet, automatically. Would that still occur on this replacement?

Yes, Android 6.0.1 also arrived on the Nexus 7 from 2013, so you can update it.
Normally you get a notification tellling you that a new update is ready to be downloaded and installed. So yea, this should still happen on the refurbished one.